Algebra Examples

$\frac{x}{14} - \frac{3}{7} \geq 2$

Step 1

Solve $x \geq 34$ .

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Step 1.1

Move all terms not containing $x$ to the right side of the inequality.

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Step 1.1.1

Add $\frac{3}{7}$ to both sides of the inequality.

$\frac{x}{14} \geq 2 + \frac{3}{7}$

Step 1.1.2

To write $2$ as a fraction with a common denominator, multiply by $\frac{7}{7}$ .

$\frac{x}{14} \geq 2 \cdot \frac{7}{7} + \frac{3}{7}$

Step 1.1.3

Combine $2$ and $\frac{7}{7}$ .

$\frac{x}{14} \geq \frac{2 \cdot 7}{7} + \frac{3}{7}$

Step 1.1.4

Combine the numerators over the common denominator.

$\frac{x}{14} \geq \frac{2 \cdot 7 + 3}{7}$

Step 1.1.5

Simplify the numerator.

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Step 1.1.5.1

Multiply $2$ by $7$ .

$\frac{x}{14} \geq \frac{14 + 3}{7}$

Step 1.1.5.2

Add $14$ and $3$ .

$\frac{x}{14} \geq \frac{17}{7}$

Step 1.2

Multiply both sides by $14$ .

$\frac{x}{14} \cdot 14 \geq \frac{17}{7} \cdot 14$

Step 1.3

Simplify.

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Step 1.3.1

Simplify the left side.

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Step 1.3.1.1

Cancel the common factor of $14$ .

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Step 1.3.1.1.1

Cancel the common factor.

$\frac{x}{14} \cdot 14 \geq \frac{17}{7} \cdot 14$

Step 1.3.1.1.2

Rewrite the expression.

$x \geq \frac{17}{7} \cdot 14$

Step 1.3.2

Simplify the right side.

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Step 1.3.2.1

Simplify $\frac{17}{7} \cdot 14$ .

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Step 1.3.2.1.1

Cancel the common factor of $7$ .

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Step 1.3.2.1.1.1

Factor $7$ out of $14$ .

$x \geq \frac{17}{7} \cdot (7 (2))$

Step 1.3.2.1.1.2

Cancel the common factor.

$x \geq \frac{17}{7} \cdot (7 \cdot 2)$

Step 1.3.2.1.1.3

Rewrite the expression.

$x \geq 17 \cdot 2$

Step 1.3.2.1.2

Multiply $17$ by $2$ .

$x \geq 34$

Step 2

Use the inequality $x \geq 34$ to build the set notation.

${x | x \geq 34}$

Step 3